“How many tennis balls does it take to fill an Olympic-sized swimming pool?”
If you’ve got some interview experience under your belt, you will no doubt have come across the “brainteaser” question.
This is the style of curveball question which is usually totally unrelated to the role you are applying for, and has an answer which is practically impossible to know.
So why do interviewers insist on throwing these questions at candidates, and how on Earth are you meant to answer them?
There are two good reasons for interviewers to deploy them.
First off, brainteasers put the candidate under pressure. And putting a candidate under pressure in an interview situation is a standard way to test how someone would handle themselves in a real-world situation.
When faced with an absurd question whose precise answer is unknowable, an unprepared interviewee will often go into meltdown. They’ll scrabble around in a state of panic, desperately hunting for the ‘right’ answer. This can usually be enough to derail the rest of the interview as well, and so it’s game over.
Staying calm and refusing to be flustered is therefore the first aspect that you need to get right.
Secondly, the brainteaser is an effective way to test for a whole variety of job-relevant skills: logic, reasoning, analysis, spatial awareness, mental arithmetic, creativity, visualisation to name a few. Most real world challenges that you can face as an employee will require at least a few of these skills. Testing for these is therefore a smart way for the interviewer to simulate your capacity to handle yourself in the role.
To be clear, the interviewer is not usually expecting any right answer. It is how you get to the answer which is the measure of success.
So, now that you understand the ‘why’, what about the ‘how’?
The good news is that, irrespective of the specific question, there is a simple 4-step process which will ensure you can handle these questions with ease:
Write down the question. You did bring a pen and notebook, right? By writing down the question you ensure that your full focus is then available to answer the question. Writing it out can also help any visualisation, and avoids you answering the wrong question!
Clarify anything uncertain. So for example, if the question is about the height of stacked objects, make sure it is clear which way the object is stacked.
Explain any thinking out loud. The question is thrown at you to help the interviewer observe your capacity to think clearly under pressure. So share how you think about working towards the answer. As mentioned already, there is usually no ‘right answer’, but if you don’t share your thought process, you have almost no chance to impress the interviewer.
Break the question down into stages. These questions normally involve measurable quantities, volumes, distances etc. So think how you can break the question into small pieces. If you can solve each of those smaller pieces, you will have a better chance to come up with a sensible answer to the whole question. Smaller pieces are also less daunting, so you are less likely to lose your nerve. And don’t forget to use your pen and paper to note down your working.
By following these 4 steps, you should be able to build towards a sensible answer which leaves your interviewer impressed.
Now that we have this simple framework, let’s take another look at the question I asked at the top, and use this process to work towards an answer:
“How many tennis balls does it take to fill an Olympic-sized swimming pool?”
This breaks down into a straightforward calculation involving the following – the volume of an Olympic-sized swimming pool (length and width and depth), the volume of a tennis ball, and an assumption about the air spaces between the balls – i.e. how tightly the balls can be packed.
It is quite likely that you don’t happen to have any of these dimensions memorised (I certainly don’t!). You might know that an Olympic pool is 50m long, but as for width and depth, and the uniformity of depth (is there a shallow and a deep end?) who knows? This actually doesn’t matter, just state aloud to the interviewer your assumptions. Say there are 8 lanes in the pool, and each lane is 2m wide which seems reasonable. And let’s assume the pool depth is, on average, 2m, up to the lip of the pool. So we state the pool dimensions as being 50m long x 16m wide x 2m deep.
Next up, the tennis balls. Let’s assume for the moment that the balls are stacked directly on top of each other. We’ll estimate that a tennis ball has a diameter of 8cm. A useful number to start with is then to calculate how many tennis balls just one layer high would fit on the floor of the pool. That’s a simple product of length and width so 50m / 8cm is 625 balls in a length, 16m / 8cm is 200 balls in a width. So 125,000 balls for one layer.
Multiply that amount by 25 layers and we have the answer: 3,125,000 balls.
So hopefully you can see how this framework helps you go from what seems like a ridiculous question, to one where a definite answer is possible once you break the problem down into small parts, solve them sequentially, while stating your assumptions. The trick is to not get worried about not knowing specific accurate dimensions, and just make reasonable assumptions. After that, it’s a simple arithmetic challenge.
As I said at the start, this is not about getting a unique answer right. Indeed a more complex (and smarter) answer would be to acknowledge a more efficient way of stacking the balls so that there is less air in the pool volume. That would allow us to stack perhaps 20% more layers of balls i.e. 30 rather than 25 in a 2m depth. So is a ‘better’ answer then 3,750,000 balls?
Well not quite, because if we stack in this more efficient method, then every even layer of balls will be smaller than every odd layer, because of how the balls nestle in the gaps. For each odd layer there are only 624 balls in a length and 199 balls in a width, so the layer has 124,176 balls.
Therefore we need to sum 15 even layers of 125,000 balls, and 15 odd layers of 124,176 balls. That totals 1,875,000 plus 1,862,640 balls which is 3,737,640 balls.
This more refined answer shows that we have genuinely visualised the problem well, and calculated the best possible answer based on the knowledge available to us. And by explaining our reasoning throughout, we have showcased a range of key skills that have served us well under pressure.
And that is how to truly nail the brainteaser!
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